Optical element-use resin composition, optical element, and projection screen

ABSTRACT

There are provided an optical element resin composition, an optical element, and a projection screen that, even upon the application of pressure to the surface of a lens in the optical element, do not cause collapse of the shape of the lens and, even when the shape of the lens has been collapsed, enable the collapsed shape to be immediately returned to the original shape, and can ensure good quality (that is, have high friction resistance). The optical element resin composition is a resin composition for constituting an optical element, which has a glass transition temperature of 5 to 36° C. and an equilibrium modulus of elasticity of 0.859×10 8  to 3.06×10 8  dyne/cm 2 .

TECHNICAL FIELD

The present invention relates to a resin composition for constituting anoptical element and more particularly to an optical element resincomposition and an optical element comprising said resin compositionthat, even upon the application of pressure to the surface of a lens inthe optical element, do not cause collapse of the shape of the lens and,even when the shape of the lens has been collapsed, enable the collapsedshape to be immediately returned to the original shape, and can ensuregood quality (that is, have high friction resistance).

BACKGROUND ART

An optical element has a construction comprising a transparent substrateand a resin composition layer, which has been shaped into an opticalshape, provided on the transparent substrate, or a constructioncomprising a resin composition layer in which an optical shape has beenprovided directly on the resin composition layer without the provisionof any substrate. There are various optical shapes which may be providedon the surface of an optical element. In general, however, aconstruction, in which fine lens-shaped projection parts have beenarranged, that is, a large number of concaves and convexes are presentwhen viewed as a whole of an optical element, is in many cases adopted.

In some cases, a plurality of optical elements are used in combination.When such lenses are used in combination, from the viewpoints ofmaximizing the optical effect of the optical elements and protecting thelens surface of the optical elements, a method is often adopted in whichthe optical elements are brought into intimate contact with each otherin such a manner that the surface of one of the optical elements facesthe surface of the other optical element. A most typical example of thiscombination is a combination of a Fresnel lens with a lenticular lensfor use in projection screens. The Fresnel lens has the function ofcollimating projected light to vertically correct the light. On theother hand, the lenticular lens has the function of horizontallydiffusing the light collimated by the Fresnel lens. In this type ofprojection screen, in use, the Fresnel lens (circular Fresnel convexlens) on its light outgoing surface side is generally brought intointimate contact with the lenticular lens on its light incident surfaceside.

In this way, when lens surfaces of optical elements are brought intointimate contact with each other, since both the surfaces have concavesand convexes, the surface shape of one of the optical elements affectsthe surface shape of the other optical element and vice versa. Forexample, in the above example, the section of the Fresnel lens surfaceis in a saw blade-like concave-convex form having a pointed apex, whilethe section of the lenticular lens surface is in an arch-likeconcave-convex form which is rounded and raised, for example, issemicircular or semielliptical. When the Fresnel lens sheet having theabove sectional form is brought into intimate contact with thelenticular lens sheet having the above sectional form, the raised top ofthe lenticular lens comes into contact with the pointed apex of theFresnel lens. In this case, the contact pressure developed at that timecauses deformation of the shape of the lenticular lens and/or the shapeof the Fresnel lens. That is, the shape of concaves and convexes on thesurface of the lens is deformed, resulting in collapsed lens.

The problem of the deformation of the lens shape can be solved byenhancing the hardness of the resin constituting the lens. Merelyenhancing the hardness of the resin, however, disadvantageously rendersthe resin fragile and leads to a problem of increased susceptibility tobreaking of the lens during handling or cutting. For this reason, theresin constituting the lens should have, on one hand, high hardness and,on the other hand, a certain level of flexibility.

The hardness of the cured resin is generally related to glass transitiontemperature. When the glass transition temperature is excessively low,the rubber elasticity lowers and, in this case, upon the application ofpressure, the resin undergoes plastic deformation. In general, when theresin has a certain level of crosslinking density, rubber elasticitydevelops even in the case of low glass transition temperature and, inthis case, even upon exposure to pressure, plastic deformation does notoccur. In the resin composition for an optical element, however, a stiffchain of a benzene ring or an alicyclic group should be introduced intothe molecular chain for refractive index improvement which is anessential requirement to be satisfied. This disadvantageously leads toincreased glass transition temperature. Therefore, it is very difficultto lower the glass transition temperature to a temperature around roomtemperature while maintaining the desired refractive index. On the otherhand, an excessively high glass transition temperature is advantageousfrom the viewpoint of improving the refractive index, but on the otherhand, the rigidity of the resin becomes so high that the internal stress(strain) is likely to remain unremoved. Therefore, in the case of a lenssheet having a structure comprising a resin composition layer laminatedonto a substrate, the relaxation of the lens resin causes warpage of thelens sheet.

On the other hand, when a material containing a halogen compound such asa bromine compound or sulfur is used, the refractive index can beenhanced without use of any aromatic compound such as a compound havinga benzene ring and, at the same time, the material properties can besuccessfully controlled. From the viewpoint of environmental load,however, it is preferred not to use bromine.

Further, when, for example, a projection screen comprising a combinationof two optical elements is transported, the optical elements are rubbedagainst each other for a long period of time while dynamic sliding ofthe optical elements against each other. Therefore, there is a fear ofproducing scratches on the surface of the optical elements. Further,during transportation or storage or during temporary storage before thestep of incorporation in TV sets, projection screens or the like are puton top of each other. In this case, since the lens surface is in a highpressure applied state for a long period of time, lenses are likely todeform due to creeping, leading to a fear of collapse of the lens.Furthermore, the internal temperature of transportation containers orholds sometimes rises and sometimes falls. Therefore, since the opticalelements are placed under high temperature environment or lowtemperature environment, the surface of the optical elements is likelyto be deformed or scratched.

Japanese Patent Laid-Open No. 010647/1998 discloses a lens sheetcomprising a cured product of an actinic radiation curable resin inwhich the modulus of elasticity of the lens sheet is in the range of 80to 20000 kg/cm² at −20 to 40° C. The claimed advantage of this lenssheet is excellent shape stability over a wide temperature range andretention of optical characteristics.

Japanese Patent Laid-Open No. 228549/2001 proposes a resin compositionfor a lens sheet in which the dissipation rate (tan δ) of the dynamicmodulus of elasticity of the ionizing radiation cured resin constitutingthe lens is brought to a predetermined range by taking intoconsideration the case where dynamic force is applied to the lens sheet.The claimed advantage of this resin composition is not to accumulatestrain and to have excellent flexibility and restorability.

However, it should be noted that the modulus of elasticity adopted inJapanese Patent Laid-Open No. 010647/1998 is one specified in JIS K7113. Since this modulus of elasticity is tensile modulus of elasticityfor a flat film, it is difficult to say that the modulus of elasticityin this publication reproduces the modulus of elasticity under actualservice conditions of the cured resin constituting the optical elementin which the cured resin undergoes compressive force.

Collapse of the lens caused by the application of pressure to the lenssurface for a long period of time can be easily avoided by using, as thematerial for the lens of the optical element, a curable resin materialwhich upon curing can be brought to a highly hard and rigid cured resin.Since, however, the rigidity of the resin is high, when the opticalelements are placed under low temperature environment duringtransportation, one of the lenses in contact with each other is likelyto damage another lens in contact with this lens. Further, when highpressure is applied to the optical element for a long period of time insuch a state that the two lenses are stacked on top of each other(lateral loading), upon the application of energy on a level beyondelastic deformation region to the lenses, the resin undergoes plasticdeformation, resulting in collapsed lenses.

Furthermore, when the crosslinking density, modulus of elasticity andthe like of the resin composition constituting the Fresnel lens areexcessively high, the internal strain added in the production process isincreased. In the Fresnel lens, the thickness of the lens sheet ispreferably small from the viewpoint of suppressing a double image. Inthis thin lens sheet, since the substrate is dragged by the influence ofinternal strain of the lens layer part, a proper curvature required ofthe lens cannot be disadvantageously held. Thus, in a lens sheet havinga relatively wide area, the use of a material having a low modulus ofelasticity is preferred from the viewpoint of reducing the internalstrain of the lens layer.

Further, in such a state that the concaves and convexes on the surfaceof the Fresnel lens have been deformed and collapsed by contactpressure, the application of vibration to the Fresnel lens increases thefrictional force (static frictional force) between both the lenses,induces stick-slip motion, and is likely to cause friction. In order tosolve this problem, for example, Japanese Patent Laid-Open Nos.384258/2000 and 59535/1997 describe that enhancing the restoring forceof a resin composition for a lens is preferred for Fresnel lensapplications. In these publications, however, there is no specificdescription on the effect attained and on the numerical value of therestoring force required.

Accordingly, an object of the present invention is to provide an opticalelement resin composition, an optical element, and a projection screenthat, even upon the application of pressure to the surface of a lens inthe optical element, do not cause collapse of the shape of the lens and,even when the shape of the lens has been collapsed, enable the collapsedshape to be immediately returned to the original shape, and can ensuregood quality (that is, have high friction resistance).

DISCLOSURE OF THE INVENTION

As a result of extensive and intensive studies with a view to solvingthe above problems of the prior art, it was found that frictionresistance can be improved by imparting elastomeric restorability(restoring force, restoring speed) to a cured resin having predeterminedoptical characteristics and that, even when a resin composition, intowhich a large amount of a benzene ring has been introduced, has beenused for desired refractive index development purposes, there is aproperty region which develops rigidity and rubber elasticity.Specifically, it was found that the above problems of the prior art canbe solved by using, in an optical element, a resin composition, in whichthe glass transition temperature, the coefficient of friction, theequilibrium modulus of elasticity, the storage-modulus, the losstangent, the restoring speed, and the deformation level are inpredetermined respective ranges and, in addition, there are apredetermined relationship between elastic deformation rate andcompression modulus of elasticity and a predetermined relationshipbetween compression modulus of elasticity and creep deformation.

Thus, according to the present invention, there is provided an opticalelement resin composition having a glass transition temperature(hereinafter referred to as “Tg”) of 5 to 36° C. and an equilibriummodulus of elasticity of 0.859×10⁸ to 3.06×10⁸ dyne/cm².

Preferably, the above optical element resin composition satisfies arelationship represented by formula We >−0.0189E+34.2 wherein Werepresents elastic deformation rate in %; and E represents compressionmodulus of elasticity in Mpa. The use of this resin can suppress thecollapse of lenses caused by mutual compression of the lens surfaces inthe projection screen. Specifically, the optical element using the resincomposition according to the present invention, even when brought intointimate contact with a warped lenticular lens, does not undergocollapse of the concave/convex parts on its lens surface. In a region ofWe≦−0.0189E+34.2, restorability from collapse of the lens surfacescaused by mutual compression is poor.

More preferably, the resin composition satisfies a relationshiprepresented by formula V≧0.178DM−0.852 wherein V represents restoringspeed in μm/sec; and DM represents maximum deformation level in μm.Satisfying a relationship represented by formula V≧0.112DM−0.236 isparticularly preferred. When the resin composition used satisfies theabove relationship between the maximum deformation level and therestoring speed, the collapse of lenses caused upon contact with alenticular lens can be suppressed. Further, specifying the relationshipbetween the deformation level of the resin and the speed of restorationof the deformation so as to fall in a predetermined range can reducefriction between lenses caused by periodical impact during vibration ofthe lenses.

In a preferred embodiment of the present invention, the optical elementresin composition satisfies a relationship represented by formulaV≧0.858R−0.644 wherein V represents restoring speed in μm/sec; and Rrepresents residual deformation level in μm. When a resin composition,in which the relationship between the restoring speed and the residualdeformation level satisfies a requirement of the above relationalexpression, is used, the collapses of the lenses caused by mutualcompression of the lens surfaces can be suppressed. Specifically, aFresnel lens can be provided which, even when brought into intimatecontact with a warped lenticular lens, does not undergo collapse of thelens. Further, in this Fresnel lens, even when once the lens is deformedas a result of stacking in a combination with a lenticular lens, uponrelease of the load (upon incorporation in TV), the lens shape can berestored to the original shape.

Further, preferably, the optical element resin composition satisfies arelationship represented by formula (−0.026E+3)<C<(−0.02E+63) wherein Crepresents creep deformation rate in %; and E represents compressionmodulus of elasticity in Mpa. The use of this resin can suppress thecollapse of lenses caused by mutual compression of the lens surfaces ina projection screen. Specifically, a Fresnel lens can be provided which,even when brought into intimate contact with a warped lenticular lens,does not collapse. In a region of C>−0.02E+63 or C<−0.026E+3, any lenshaving proper creep resistance with respect to collapses of lensescaused by mutual compression of the lens surfaces cannot be provided.

In a particularly preferred embodiment, the optical element resincomposition according to the present invention has a storage modulus ofnot more than 2.96×10¹⁰ dyne/cm² at −20° C. and a loss tangent of notless than 0.02 at −20° C. In the resin having the above property values,the quantity of energy stored in the vibration is small, the proportionof loss as thermal energy is high, and, thus, the vibration can easilybe relaxed. Therefore, in the lens using this resin, friction caused bydynamic contact between lenses can easily be avoided.

In a preferred embodiment of the present invention, the loss area in atemperature range of −20 to 50° C. in a curve for dependency of losstangent upon temperature is 20° C. or above. In particular, the lossarea in a temperature range of −20 to 50° C. in a curve for dependencyof loss tangent upon temperature is preferably 20 to 43.2° C.,particularly preferably 20 to 31.7° C. The use of the resin compositionhaving properties falling within the above numerical property valuerange is advantageous in that, upon exposure to vibration with variousfrequencies during transportation of the projection screen, thevibrational energy is converted to thermal energy. Therefore, veryeffective fundamental vibration proof properties can be provided. In thecase of a resin composition having a large loss area, sincepolyrelaxation of molecular motion occurs, the restorability of theresin can be improved and, thus, the deformation of the resin caused bythe external pressure can be reduced over a wide temperature range.

More preferably, the resin composition has a coefficient of dynamicfriction of 0.07 to 0.15 at room temperature. When the resin compositionhaving this property value is used, the occurrence of scratches can beeffectively prevented during transportation, particularly duringtransportation under environment of a low temperature around −20° C.Here room temperature refers to 25° C. However, it should be noted that,at 20° C., the value of the coefficient of dynamic friction remainssubstantially unchanged. When the value of the coefficient of dynamicfriction exceeds 0.15, the occurrence of scratches during transportationat a temperature around −20° C. cannot be effectively prevented. On theother hand, when the value of the coefficient of dynamic friction isless than 0.07, in order to impart slipperiness, the amount of siliconeor the like added should be considerably increased. The increase in thesilicone content disadvantageously deteriorates the adhesion of theresin composition to the substrate.

In another aspect of the present invention, there is provided an opticalelement comprising the above optical element resin composition.

Preferably, the optical element has a refractive index of not less than1.52, and this optical element can be used as a Fresnel lens sheet.

In still another aspect of the present invention, there is provided aprojection screen comprising the above optical element and a lenticularlens.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic view of a projection screen comprising an opticalelement;

FIG. 2 is a schematic view illustrating a curve for dependency ofpenetration depth upon load;

FIG. 3 is a schematic view showing an indenter action site;

FIG. 4 is a graph showing a PSD waveform used in a vibration test;

FIG. 5 is a schematic view illustrating a curve for dependency ofpenetration depth upon load;

FIG. 6 is a graph in which the relationship between the glass transitiontemperature and the equilibrium modulus of elasticity of resincompositions used in Examples and Comparative Examples has been plotted;

FIG. 7 is a graph in which the relationship between the elasticdeformation rate and the compression modulus of elasticity of resincompositions used in Examples and Comparative Examples has been plotted;

FIG. 8 is a graph in which the relationship between the compressionmodulus of elasticity and the creep deformation rate of resincompositions used in Examples and Comparative Examples has been plotted;

FIG. 9 is a graph in which the relationship between the maximumdeformation level and the restoring speed of resin compositions used inExamples and Comparative Examples has been plotted; and

FIG. 10 is a graph in which the relationship between the residualdeformation level and the restoring speed of resin compositions used inExamples and Comparative Examples has been plotted.

BEST MODE FOR CARRYING OUT THE INVENTION

FIG. 1 is a typical diagram showing a projection screen using a Fresnellens sheet as a typical optical element according to the presentinvention. In a projection screen 1, a Fresnel lens sheet 2 and alenticular lens sheet 3 are provided and brought into intimate contactwith each other so that a lens surface 2 c of the Fresnel lens sheet 2faces a lens surface 3 c of the lenticular lens sheet 3. In FIG. 1, forboth the sheet 2 and the sheet 3, a separate substrate is provided.Specifically, a lens layer 2 b is stacked on a substrate 2 a, and a lenslayer 3 b is stacked on a substrate 3 b. In each of the lens sheets,however, instead of the construction in which the substrate and the lenslayer are provided separately from each other, a construction may beadopted in which the substrate is provided integrally with the lenslayer. Further, as shown in FIG. 1, the lenticular lens sheet 3 may havemicrolenticular lenses and projections and black stripes on its sideremote from the Fresnel lens sheet 2.

In addition to the lenticular lens and the Fresnel (convex) lensdescribed in conjunction with FIG. 1, lenses having any optical shapesuch as Fresnel concave lenses, prisms, or mesh lenses may also beprovided in the optical element. Further, one optical element may have,on its both sides, optical element surfaces having identical ordissimilar optical shapes.

In the present invention, the optical element resin compositionconstituting the whole optical element or, in the case of an opticalelement comprising a lens layer provided on a substrate, constitutingthe lens layer is specified by various parameters mentioned below. Theoptical element comprising the resin composition according to thepresent invention is typically a Fresnel lens sheet. This opticalelement, particularly a Fresnel lens sheet, may be used in combinationwith a lenticular lens sheet to constitute a projection screen. Theoptical element resin composition referred to herein refers directly toone in the form of a product or refers to one in the form of a thinresin sheet or a lens layer in the case where the resin composition isused for measurement. However, it should be noted that the opticalelement resin composition embraces uncured compositions satisfyingvarious parameter requirements mentioned below, for example, in a formbefore product production, or in the form of a thin sheet formeasurement purposes.

The optical element resin composition preferably comprises an ionizingradiation curable material composed mainly of an oligomer and/or amonomer of an ionizing radiation curable radically polymerizableacrylate compound or an oligomer and/or a monomer of a cationicallypolymerizable epoxy compound, a vinyl ether compound, or an oxetanecompound and optionally additives for curing such as ultravioletpolymerization initiators and photosensitizers. A mixture of theradically polymerizable compound with the cationically polymerizablecompound may also be used. The additive for curing undergoesdecomposition during polymerization of the resin composition. Therefore,a decomposition product thereof remains after curing the resin.

On the other hand, when a maleimide derivative is used instead of thepolymerization initiator, curing occurs with high efficiency. Therefore,in this case, a residue is less likely to remain, and, thus, this methodis more preferred from the viewpoints of energy saving andenvironmentally friendly nature. Further, a thermoplastic resin may beincorporated with a view to improving the properties of the product.

Further, the radically polymerizable resin preferably contains a thiolcompound. In this case, continuous growth and chain growthpolymerization take place in cooperation by a thiol-ene reaction.Therefore, the homogeneity of the phase within the cured film isimproved, and material properties such as toughness, flexibility, andhardness and adhesion to the substrate are improved.

The optical element resin composition may contain various additiveswhich can be added in the production of ordinary sheet-like orplate-like resin products. Further, the optical element resincomposition may contain light diffusing agents, colorants and the likefrom the viewpoint of improving optical properties of the opticalelement.

Since the contact pressure developed by the warpage of the lenticularlens affects compression load to the Fresnel lens, specifying thecompression modulus of elasticity has great significance. Additionallyspecifying the creep deformation rate under compression loading is veryeffective as means for reducing the lens collapse phenomenon of theFresnel lens caused by applying a load for a long period of time (seeJapanese Patent Application No. 126650/2001). The above means issuitable for materials having high rigidity and high energy elasticity,but on the other hand, the application of the above means to materialshaving entropy elasticity such as rubber elasticity is difficult. Theresin having rubber elasticity is excellent in low-temperature hardness,vibration damping properties, and restorability after the application ofhigh pressure for a long period of time. However, merely specifyingcreep deformation rate and compression modulus of elasticity asproperties of this resin does not suffice. In the present invention, itwas found that, when the resin composition has a predeterminedcompression modulus of elasticity and a predetermined elasticdeformation rate, materials having excellent restorability from lensdeformation caused by contact pressure can be realized. Further, it wasclarified that the crosslinking density causes a significant differencein restorability.

Specifically, in the resin composition according to the presentinvention, when a material having a low glass transition temperature isused, the resin can be converted from a glass region to a rubber regionat the service temperature of the lens to develop a predetermined levelof elastic deformation (rubber elasticity). What is most preferred forlowering the creep deformation level to impart a certain level ofelastomeric restoring force is to optimize the crosslinking density ofthe resin as the material used to provide a network structure with ahomogeneously dispersed proper network.

Parameters which specify the optical element resin composition accordingto the present invention are (1) glass transition temperature, (2)equilibrium modulus of elasticity, (3) elastic deformation rate, (4)compression modulus of elasticity, (5) restoring speed, (6) maximumdeformation level, (7) residual deformation level, and, if necessary,further (8) creep deformation rate, (9) storage modulus, (10) losstangent, and (12) coefficient of dynamic friction.

Among the above parameters, parameters (1), (2), (9), and (10) can becalculated based on the results of the measurement of dynamicviscoelasticity, and parameters (3) to (8) can be calculated based onthe results of measurement with a microhardness tester. These parameterswill be described below.

In the measurement of the dynamic viscoelasticity, a resin sheet of anoptical element resin composition having predetermined thickness isprepared as a sample. When an ultraviolet curable resin composition isused to prepare the resin sheet, the resin is cured by ultravioletirradiation. The storage modulus and the loss tangent are measured whilevarying the temperature with a dynamic viscoelastometer and applyingvibration at constant cycle periods in a major axis direction of thesample. Based on the relationship between the storage modulus and thetemperature, the storage modulus at a predetermined temperature and theequilibrium modulus of elasticity in an equilibrium state aredetermined. Based on the relationship between the loss tangent and thetemperature, the loss tangent at a predetermined temperature iscalculated.

The storage modulus is related to the ability of elastically storingenergy with respect to strain applied to the material and is a kind ofdynamic properties and a measure of elastic properties of the material(resin composition). The loss tangent is determined based on the lossmodulus/storage modulus. The loss modulus represents viscous propertiesof the material (resin composition), is related to the quantity ofenergy with respect to dissipation, as heat, of the material duringdeformation, and is a measure of relaxation of vibration energy. At atemperature at or above maximum loss tangent temperature, polymersegments of the resin are in a fully relaxed state, and the storagemodulus component at that time is derived from crosslink points aslinking parts. Therefore, the equilibrium modulus of elasticity as thestorage modulus in the rubber elasticity region is related to thecrosslinking density of the resin. The temperature corresponding to themaximum value of the loss tangent in a curve for the dependency of losstangent upon temperature is said to represent phase transition of thematerial and approximately corresponds to the glass transitiontemperature which represents transition from glass region to rubberregion. The glass transition temperature can also be measured by DSC(differential scanning calorimetry) in which the difference in energyinput between the material and a reference material is measured as afunction of the temperature (a DSC curve or a DTA curve) while varyingthe temperature of the material and the reference material and the phasetransition temperature is determined from the endothermic behavior.

Further, detailed information on structures and properties of polymericmaterials such as micro-Brownian motion as motion of the molecularchain, rotation of side chain, and rotation of terminal groups, and,further, phase transition of homopolymers can also be obtained bydielectric relaxation measurement over a wide temperature range and awide frequency range. Therefore, the above information may be reflectedinto the design of resins. Specifically, as described in Japanese PatentNo. 3318593, in order to absorb vibration by conversion of vibrationenergy to thermal energy, the evaluation of the orientation of dipolescaused by an electric field is important, and the resin can easily bedesigned by taking mechanical relaxation derived from dielectricrelaxation into consideration.

The cured product of the resin composition for constituting the opticalelement according to the present invention has a glass transitiontemperature of 5.0 to 36.0° C. and an equilibrium modulus of elasticityof 0.859×10⁸ to 3.06×10⁸ dyne/cm². In the optical element using thisresin composition, even upon the application of pressure to the lenssheet surface, the lens surface is not collapsed and good quality can beensured.

Even when the glass transition temperature of the cured product is inthe above-defined range, if the equilibrium modulus of elasticityexceeds 3.06×10⁸ dyne/cm², then the crosslinking density is increased.Therefore, in this case, the motion of the molecular chain whichdevelops a viscous structure is frozen, resulting in deterioratedrestorability of the resin. That is, the resin is rendered rigid and isrendered less susceptible to deformation by increasing the crosslinkingdensity of the molecular chain. Merely increasing the crosslinkingdensity, however, is disadvantageous in that, when the resin is oncedeformed by a large load, the resin is less likely to be returned to theoriginal state. For this reason, the resin having an equilibrium modulusof elasticity above value can withstand neither contact pressure appliedin the superposition of two lens sheets to form a projection screen norhigh pressure applied in sheet loading at the time of transportation ofa package of lens sheets and at the time of assembling of the screen inTV.

Further, for the cured product of the resin according to the presentinvention, the glass transition temperature representing the transitionfrom glass region to rubber region is around room temperature (25° C.),and, thus, the cured product of the resin is highly flexible at thetemperature of environment in which the sheets are usually handled. Whena resin composition having the above glass transition temperature andthe equilibrium modulus of elasticity is used, a modulus of elasticity,which is considerably above that of the conventional resin for anoptical element, can be ensured while maintaining the flexibility of themolded product of the resin. This resin composition can be provided byoptimizing the crosslinking density to realize a homogeneously dispersednetwork structure in the molecular structure of the resin. Thecrosslinking density can be optimized by (i) regulating the mixing ratioof monofunctional, bifunctional, trifunctional, and higherpolyfunctional monomers, (ii) selecting monomers having functionalgroups having structures contributable to toughness, for example,ethylene oxide-modified monomers, propylene oxide-modified monomers,glycolic monomers such as diethylene glycol diacrylate or polyethyleneglycol diacrylate, and diol monomers such as 1,4-butanediol diacrylateor 1,6-hexanediol diacrylate, and regulating their mixing ratio andmolecular weight, or (iii) regulating the mixing ratio or molecularweight of epoxy (meth)acrylate oligomers or urethane (meth)acrylateoligomers. In the case of radical polymerization, in order to avoid thepresence of double bond remaining unreacted due to its high reactionrate, from the viewpoint of homogeneous dispersion of the networkstructure, care should of course be taken when using a penta-, hexa- orhigher functional monomer.

Further, in order to realize a homogeneous network structure, the lengthof the molecular chain between crosslink points should also be takeninto consideration. Specifically, attention should also be paid to theregulation of the repetition of polyether chains and polyester chains ina urethane oligomer, the regulation of the repetition of ethylene oxidechains, propylene oxide chains or the like in monomers, and themolecular weight distribution and mixing ratio thereof.

Rubber-like materials generally comprise long-chain molecules, and thestructure thereof is such that the long-chain molecules are mutuallybonded through weak van der Waals force (secondary bonding force) and,further, bridges (crosslinks) formed by valence bonds are provided inplaces between long-chain molecules. Each part of chain molecules ofrubber has a gap (space) inherent in rubber, and movement of thelong-chain molecule to the gap causes molecular motion. In this case,however, since the molecular chain is fixed by the crosslink point, freedeformation of the whole molecular chain by macro-Brownian motion isretricted. On the other hand, when the crosslink point is absent, in atemperature region above the glass transition temperature, theelasticity is lost by the macro-Brownian motion of the molecular chain.However, when a large number of crosslink points are present and bondingforce between chains is excessively strong, disadvantageously, irregularmotion in a relatively small area of each part of chain molecules(micro-Brownian motion) is also suppressed, making it impossible todevelop rubber elasticity. That is, what is important for development ofrubber elasticity is to promote micro-Brownian motion while suppressingmacro-Brownian motion. The crosslinking density should be regulated forthe suppression of macro-Brownian motion. In this case, homogenousdistribution of the crosslink points is also important. On the otherhand, in order to promote micro-Brownian motion, the glass transitiontemperature should be regulated. A highly resilient high-refractiveindex curing resin, which is less likely to cause collapse of thescreen, can be provided by designing materials while taking intoconsideration a temperature region in which the projection screen isusually employed. That is, in the present invention, an optical elementresin composition having flexibility (rubber elasticity) suitable foruse in a projection screen is provided by designing materials from theviewpoints of the crosslinking density and the glass transitiontemperature based on the above molecular study.

The resin composition according to the present invention preferablysatisfies a relationship represented by formula We>−0.0189E+34.2 whereinWe represents elastic deformation rate in %; and E representscompression modulus of elasticity in Mpa.

Further, the resin composition according to the present inventionpreferably satisfies a relationship represented by(−0.026E+3)<C<(—0.02E+63) wherein C represents creep deformation rate in%; and E represents compression modulus of elasticity in Mpa.

The elastic deformation rate (elastic work level), the compressionmodulus of elasticity, and the creep deformation rate will be described.These material property parameters can be calculated by applying auniversal hardness test with a microhardness meter. Specifically, theload applied by an indenter is gradually increased to a predeterminedvalue and is then gradually decreased to determine a curve for thedependency of penetration depth upon load, and the curve thus obtainedis analyzed for calculation of the property parameters.

Regarding the optical element resin composition, the whole moldedproduct of the resin should be flexible and restorable at roomtemperature, and deformation caused by pressure cannot be fully relaxedby a part of the molded product of the resin (a part of lens). That is,in the projection screen, the Fresnel lens and the lenticular lens arein partial contact with each other, and the whole assembly is supportedby the contact points. In general, in order that the whole moldedproduct of the resin has flexibility and restorability from theviewpoint of returning the deformed state to the original undeformedstate, the whole cured product should have a structure capable ofrelaxing dynamical deformation, and, at the same time, this structureshould be present in the matrix so that the plastic component is notaffected by external force. Accordingly, any different index of theflexibility and the restorability is necessary. In the presentinvention, the elastic deformation rate as a parameter of the elasticwork level is used as a parameter for the flexibility and therestorability.

Material property values such as elastic deformation rate can beevaluated by a universal hardness test. Specifically, a measuring methodfor determining universal hardness is applied. In this test, an indenteris indented into the surface of the sample, and, in a load appliedstate, the depth of indentation is directly read. Specifically, variousproperties of the resin film can be determined by gradually increasingor decreasing the load to a set value rather than the measurement of thedepth of indentation by the indenter for only one point. (See“Evaluation of material property values by the universal hardness test”,Zairyo Shiken Gijutsu, Vol. 43, No. 2, April, 1998).

Further, in the present invention, the collapse of lenses caused bycontact pressure is reduced by using a resin composition in which therelationship between the elastic deformation rate and the modulus ofelasticity of the resin composition falls within a predetermined range.

Furthermore, in the present invention, it is important for the restoringspeed of the resin composition to have a predetermined relationship withthe maximum deformation level of the resin composition.

The restorability can be evaluated in terms of elastic deformation rate.In the elastic deformation rate, however, evaluation on an absolutescale depending upon an actual deformation level cannot be provided. Onthe other hand, evaluating the level of storability from a certaindeformation level based on the maximum deformation level and therestoring speed is very important. Specifically, in the case of a smallmodulus of elasticity, if the restoring speed is high despite a highlevel of deformation, then the proportion of the elastic work is highand the restorability is high. On the other hand, in the case of largemodulus of elasticity, since the deformation is small and energy isstored, the proportion of the elastic work is high. In this case,however, when the restoring speed is low, the restorability is low.Therefore, in addition to the evaluation of the elastic deformationrate, the maximum deformation level and the restoring speed should beadded as an index to perform evaluation on an absolute scale. Thus, thelevel of the deformation of lens, which develops optical defects, or thelevel of the restorability which can avoid the observation of theoptical defects despite deformation can be clearly evaluated byevaluating the maximum deformation level.

In projection screen applications, the highest restorability is requiredin the case where a high load is applied to lenses, for example, bylateral loading of lenses during the production of the projectionscreen. In this case, in the stage of design, estimation should becarried out on the level of restoration of lens, deformed by the highload, after the release of the load. This estimation can be derived fromthe relationship of V≧0.112DM−0.236.

In a projection screen comprising a combination of a lenticular lenswith a Fresnel lens, even when the collapse of lens is present at atemperature around room temperature, the collapse of lens is eliminatedwith the elapse of time. The reason for this is believed as follows.When a warped lenticular lens is forcibly pressed against a flat Fresnellens, in an early stage, pressure is applied by the warpage of the lens.However, with the elapse of time, creeping permits the lenticular lensto conform to the plane of the Fresnel lens to reduce the contactpressure. The reason for the elimination of the collapse of lens is alsoconsidered to rely upon the following mechanism. Specifically, since thethickness of the lenticular lens is small, contact pressure biased, forexample, by strains produced at the time of lens setting is sometimesapplied. The biased contact pressure is brought to uniform contactpressure by the environmental temperature or humidity or the elapse oftime, and, consequently, local pressure is released to restore theresin.

Upon application of vibration to the collapse lenses, friction betweenthe lenses or collision of the lenses against each other increasesfrictional force (static frictional force), and, thus, abrasion of thelenses is likely to occur. Therefore, it is considered that shaperestoration immediately after deformation at the lens contact part canreduce frictional force to reduce lens abrasion. In the presentinvention, it was found that not only the collapse of the lens but alsothe lens abrasion can be effectively prevented by preparing the opticalelement using a resin composition having a predetermined relationshipbetween the restoring speed and the maximum deformation level.

Furthermore, optical defects caused by lens deformation can besuppressed by using a resin composition having a predeterminedrelationship between the restoring speed and the residual deformationlevel. That is, defects in the shape of lenses for every load can beavoided by regulating the plastic deformation level. Further, even whena certain level of permanent strain stays in the resin composition,maintaining the restoring speed on a certain level is considered toavoid the collapse of the lens and to suppress optical defects.

Furthermore, when a Fresnel lens is separated from a mold, in someseparation direction, shear force acts on the lens due to the positionalrelationship between the mold and the concave/convex part of the lens.In this case, the frictional force is large at the interface of the moldand the lens, and, upon the application of load, the lens is sometimesdeformed. Thus, in some cases, a part of the lens separated from themold is strained, resulting in optical defects. The use of an externalor internal release agent or the like to reduce frictional force at thetime of the separation of the lens from the mold is considered effectivefor reducing the optical defects. Mere use of the release agent,however, cannot cope with various optical element shapes withoutdifficulties. This necessitates the use of a resin which has excellentrestorability and is free from permanent strain. In the presentinvention, the above problem can be solved by using a resin compositionsatisfying a requirement represented by formula V≧0.858R−0.644.

When the residual deformation level is large, external force affects theviscous structure. Therefore, in this case, the restoring speed(restorability) can generally be estimated to be low. In fact, when theresidual deformation level is relatively small, the restoring speed islarge. Therefore, the deformation of the lens can be suppressed by usinga resin having a high restoring speed (high restorability). Even whenthe resin has a predetermined maximum deformation level and a certainlevel of restoring speed, in some cases, the residual deformation(permanent deformation) is relatively large. Therefore, it is importantto confirm three parameters, i.e., deformation level, restorabilitylevel, and residual deformation level. The contact pressure caused bythe warpage of the lenticular lens is reduced by creeping of the lenswith the elapse of time. However, restoring force of the Fresnel lensresin in the pressure applied state for pressing back the pressure isimportant for reducing the deformation, and the restoring speed and theresidual deformation level representing the restoring force should bediscussed.

Further, in the production of projection screen TV (in assemblingprocess), a loading step is carried out in which large-area screens areput on top of each other. Therefore, restorability and permanentdeformation rate upon load release from the lateral loading, in whichthe lenses undergo a high load, should be taken into consideration.

In mass production of projection screen TVs or the like, a large numberof sets of a combination of a lenticular lens with a Fresnel lens arestored in a mutually superimposed state. In some relationship betweenthe material of the Fresnel lens and the material of the lenticularlens, the deformation of both the lens sheets should be taken intoconsideration. For example, when the Fresnel lens is formed of a curingresin while the lenticular lens is formed of a thermoplastic resin, aresin composition having predetermined mechanical properties should beused in consideration of the deformation of the Fresnel lens. Therefore,when the resin composition according to the present invention is used inthe Fresnel lens, it can be said that a smaller residual deformationlevel is more preferred. In the present invention, however, it was foundthat, even in the case of a resin having a relatively large residualdeformation level, when the restoring speed falls within a predeterminedrange, the collapse of the lens can be suppressed.

Preferably, the optical element resin composition according to thepresent invention has a storage modulus, as dynamic viscoelasticity, ofnot more than 2.96×10¹⁰ dyne/cm² at −20° C. and a loss tangent of notless than 0.02 at −20° C. The introduction of a benzene ring into themolecular chain for purposes of enhancing the refractive index of anoptical element formed of a cured product of the resin compositionrenders the resin composition hard and fragile. Even when the resincomposition is hard at room temperature, the occurrence of scratches byfriction between optical element surfaces can be avoided to a certainextent so far as the modulus of elasticity at a low temperature is low.Further, resistance to friction between optical element surfaces at alow temperature (0° C.) or a very low temperature (−20° C.) can beimparted by specifying the loss tangent as dynamic viscoelasticity to apredetermined value range, lowering the storage modulus at a lowtemperature, and imparting slipperiness to the resin composition.

In the formation of a Fresnel lens sheet using a Fresnel mold, when ahard resin is used and the planarity of the mold fabricated by a latheis good, scratches of the molded product by friction are less likely tooccur. On the other hand, when the planarity of the mold is not good,scratches of the molded product by friction are likely to occur. In theresin composition according to the present invention, the loss tangentas the dynamic viscoelasticity is large and not less than 0.02 and thestorage modulus is small. Therefore, even when the planarity of the moldis poor and protrusion parts are present, scratches are less likely tooccur in the molded product because the energy of impact or vibration inthe protrusion parts is dispersed to control the vibration. This isconsidered attributable to the fact that the vibration transmissibilityat the resonance point of the vibration system reduces with increasingthe loss tangent value.

Loss modulus of elasticity may be mentioned as a parameter associatedwith the storage modulus. At a low temperature, increasing the value ofthe loss modulus of elasticity (increasing the loss tangent at a lowtemperature) can increase the ability of the material to dissipatevibration as heat and can reduce scratches caused by friction betweenoptical elements at a low temperature. Further, reducing the value ofthe storage modulus also can reduce scratches caused by friction betweenoptical elements at a low temperature.

When an optical element is formed of a resin having a large loss modulusof elasticity, the viscosity of the structure within the bulk of thematerial is increased. Therefore, when static external force reaches thestructure, plastic deformation is induced and, as a result, collapse ofoptical element surfaces such as lens surfaces is likely to occur. Inthe present invention, this problem is solved by using a resincomposition having a small storage modulus value.

Further, in the present invention, when the loss area of the losstangent of the resin composition is in a predetermined value range, lensabrasion caused by dynamic contact between lenses can be reduced becausevibration energy can be converted to thermal energy over a widefrequency range. During the transportation of the projection screen,vibration takes place over a wide frequency range of from a lowfrequency of about 10 Hz to a relatively high frequency of about 100 Hz.In the present invention, it was found that the loss area is preferablylarge for attaining good energy loss effect over the wide frequencyrange.

In a curve for the dependency of loss tangent upon temperature, the peakwidth, that is, the temperature dispersion width represents relaxationof molecular motion. In this case, a larger width means that themultiplicity of the relaxation is larger and viscosity attributable to arestorable structure is more likely to develop. That is, while fullytaking crosslinking density into consideration, toughness is imparted tothe resin over a wide temperature range to impart restoring force forpressing back the external force to the projection screen over a widetemperature range and consequently to reduce plastic deformation of thelens. Because of the large restoring speed, the effect can also beattained for collapse of lenses in which a large load is released.

On the other hand, when the loss area is large, the contribution of theviscosity is so large that plastic deformation is increased. As a resultof comprehensive regulation of the above various properties of lens, therelaxation is suppressed by enhancing the crosslinking density(imparting restorability) to suppress plastic deformation andintroducing a stiff straight chain to improve refractive index. That is,the upper limit value of the loss tangent is determined by thesuppression of the relaxation.

As described above, in the present invention, it was found that when theloss tangent value at a predetermined temperature is a given value orlarger, the scratch resistance can be improved. Specifically, in orderto maintain scratch resistance over a wide temperature range and over awide vibration frequency range, the loss area in a temperature range of−20 to 50° C. should be 20° C. or above, preferably 20 to 43.2° C.,particularly preferably 20 to 31.7° C. The loss area refers to an areaof a loss tangent peak in a curve for dependency of loss tangent upontemperature and can be calculated by integrating the curve with respectto a predetermined temperature range.

The optical element prepared using the above resin compositionpreferably has a refractive index of not less than 1.52. As describedabove, the refractive index may be mentioned as one of characteristicsrequired of an optical element. In order to enhance the refractiveindex, a benzene ring should be introduced into a compound constitutingthe resin composition. However, there is a trade-off relationshipbetween an improvement in refractive index and the flexibility of theresin. The optical resin prepared using the resin composition accordingto the present invention has a refractive index of not less than 0.1.52.For the optical resin composition having this refractive index, thecrosslinking density, the toughness, and the refractive index can beregulated by incorporating, in a compound having a structure containingtwo benzene rings such as bisphenol A, a predetermined amount of anethylene oxide (EO)-modified diacrylate monomer for toughnessimpartation purposes. When the regulation of the refractive index onlyis contemplated, this can be achieved by incorporating a predeterminedamount of phenoxyethyl acrylate, phenoxyethyl EO-modified acrylate,2-hydroxy-3-phenoxypropyl acrylate, p-cumyl phenol EO-modified acrylate,p-cumylphenoxyethylene glycol acrylate, bisphenol A epoxy acrylate orthe like.

In the resin composition according to the present invention, urethaneacrylates usable with the above compound include: a polyester-typeurethane acrylate produced by reacting an isocyanate compound, such astoluene diisocyanate (TDI), hexamethylene diisocyanate (HMDI), methylenediisocyanate (MDI), or isophorone diisocyanate (IPDI), with a polybasicacid such as phthalic acid, adipic acid, glutaric acid, or caprolactone,and a polyhydric alcohol such as ethylene glycol, bisphenol A,diethylene glycol, triethylene glycol, neopentyl glycol, 1,4-butanediol,or 3-methyl-1,5-pentanediol and a hydroxyl-containing (meth)acrylate;and a polyether-type urethane acrylate produced by reacting anisocyanate with a polyether polyol such as polyethylene glycol,polypropylene glycol, or polytetramethylene glycol, and a polyetherglycol and a hydroxyl-containing (meth)acrylate. When the refractiveindex is brought to 1.52 to 1.55 or more, the content of the benzenering in the compound used should be increased. In this case, however,when the content of the benzene ring is increased, the flexibility ofthe resin composition is lost. Therefore, a compound having a viscousstructure such as ethylene oxide should be incorporated in the abovecompound.

More preferably, the optical element resin composition according to thepresent invention has a coefficient of dynamic friction of 0.07 to 0.15at room temperature. When the resin composition having the abovecoefficient of dynamic friction is used, the occurrence of scratchesduring the transportation, particularly under a low-temperatureenvironment around −20° C., can be effectively prevented. Here roomtemperature refers to 25° C. However, it should be noted that, even at−20° C., the value of the coefficient of dynamic friction remainssubstantially unchanged. When the value of the coefficient of dynamicfriction exceeds 0.15, the occurrence of scratches caused duringtransportation at a temperature around −20° C. cannot be effectivelyprevented. On the other hand, when the value of the coefficient ofdynamic friction is less than 0.07, in order to impart slipperiness, theamount of silicone or the like added should be considerably increased.When the amount of the slip agent added is increased, during use invarious temperature environments, particularly during use in a hightemperature environment, the slip agent is likely to bleed out to theoutside of the lens. Further, the optical performance of the opticalelement and the adhesion between the lens and the substrate aredeteriorated.

In order to bring the value of coefficient of dynamic friction to 0.07to 0.15, a slip agent is preferably incorporated in the resincomposition. Preferred slip agents include one which does not cause anyoptical defect in the resin composition, for example, does not causelowered transmittance and bleed-out of the slip agent in ahigh-temperature environment test, one which causes migration to thesurface during molding, but on the other hand, is less likely to bleedout after curing, one in which the refractive index is as close aspossible to the refractive index of the resin composition, or one which,in the case of a particulate slip agent (silica) or the like, has aparticle diameter of not more than the wavelength of light.

Further, preferably, the additive per se has low viscosity, and, upondeposition on the substrate side, leveling can be easily carried out, orthe refractive index is close to that of the substrate. Furthermore,preferably, the additive does not sacrifice the adhesion of the resincomposition to the substrate.

Preferred slip agents of this type include silicones and siliconepolymers. The slip-agent is preferably modified silicone, morepreferably polyether-modified polydimethylsiloxane. When lens sheets areformed by curing the resin composition containing the above additive,the occurrence of scratches on the surface of lenses by friction betweenthe lens sheets can be reduced.

The content of the additive in the whole resin composition is preferably0.01 to 10% by weight. When the additive content is less than 0.01% byweight, predetermined slipperiness cannot be provided. On the otherhand, when the additive content exceeds 10% by weight, the materialproperties of the resin composition are deteriorated.

Specific examples of silicones and silicone polymers usable hereininclude: BYK-307, BYK-333, BYK-332, BYK-331, BYK-345, BYK-348, BYK-370,and BYK-UV 3510, manufactured by Bik-Chemie Japan K.K.; X-22-2404,KF-62-7192, KF-615A, KF-618, KF-353, KF-353A, KF-96, KF-54, KF-56,KF-410, KF-412, HIVACF-4, HIVACF-5, KF-945A, KF-354, and KF-353,manufactured by The Shin-Etsu Chemical Co., Ltd.; SH-28PA, SH-29PA,SH-190, SH-510, SH-550, SH-8410, SH-8421, SYLGARD309, BY16-152,BY16-152B, and BY16-152C, manufactured by Dow Corning Toray Japan Co.,Ltd.; FZ-2105, FZ-2165, FZ-2163, L-77, L-7001, L-7002, L-7604, andL-7607, manufactured by Nippon Unicar Co., Ltd.; EFKA-S018, EFKA-3033,EFKA-83, EFKA-3232, EFKA-3236, and EFKA-3239, manufactured by EFKAAdditives; and GLANOL 410 manufactured by Kyoeisha Chemical Co., Ltd.

In order to avoid bleedout of the silicone component with the elapse oftime upon a change in environment after curing of the resin, a reactivesilicone such as silicone acrylate or silicone methacrylate may be usedas an auxiliary additive in combination with the above additive.Specific examples of reactive silicones usable herein include: BYK-UV3500 and BYK-UV 3530, manufactured by Bik-Chemie Japan K.K.; BentadUV-31 manufactured by Nippon Konica Co., Ltd.; and X-24-8201,X-22-174DX, X-22-2426, X-22-2404, X-22-164A, X-22-164B, and X-22-164C,manufactured by The Shin-Etsu Chemical Co., Ltd.

Examples of commercially available products of silica particles include:SUNSPHERE NP-100 and SUNSPHERE NP-200, manufactured by Dohkai Chemicalindustries Co., Ltd.; SILSTAR MK-08 and SILSTAR MK-15, manufactured byNippon Chemical Industrial CO., LTD.; FB-48 manufactured by Denki KagakuKogyo K.K.; and Nipsil E220A manufactured by Nippon Silica industrialCo., Ltd.

EXAMPLES

Various resin compositions were used to prepare samples which were thenmeasured for the above-described various parameters. Further, sampleswere used to prepare Fresnel lens sheets which were then evaluated forpracticality. The results of measurement of the parameters and theresults of evaluation of the practicality are shown in Tables 1 to 5.The measured parameters are refractive index, glass transitiontemperature, equilibrium modulus of elasticity, elastic deformationrate, compression modulus of elasticity, maximum deformation level,residual deformation level, restoring speed, creep deformation rate,storage modulus at −20° C., loss tangent at various temperatures, lossarea, and coefficient of dynamic friction.

The evaluated items are a TV setting collapse test, a loading test, anda vibration test at various temperatures. The evaluation results areshown in Tables 1 to 5. In the tables, for items in which themeasurement temperature is not indicated, the results are those measuredat 25° C.

Resin compositions A1 to A22 described in the evaluation resultscorrespond to examples of the optical element resin compositionaccording to the present invention, and resins B1 to B27 correspond tocomparative optical element resin compositions. TABLE 1 Resin A1 ResinA2 Resin A3 Resin A4 Resin A5 Resin A6 Resin A7 Resin A8 Resin A9 ResinA10 Refractive index (D line) 1.551 1.551 1.552 1.553 1.552 1.551 1.5511.551 1.549 1.549 Compression modulus 95.29 136.3 118.8 148.7 112.9625.1 489.1 1171.3 842.5 603.4 of elasticity (Mpa) Elastic deformationrate 45.869 47.72 44.65 31.35 45.43 22.43 19.16 18.85 34.3 36.86 (%)Crosslinking density 1.01E+8  1.15E+8  1.18E+8  0.97E+8  1.58E+8 1.31E+8  1.07E+8  1.29E+8  1.77E+8  1.44E+8  (dyne/cm²) (1 Hz: 80° C.)Glass transition temp. 22.6 19.5 22.9 23.7 22.2 29.8 34.5 30.6 27.1 23.9(Tp) Creep deformation rate 8.859 10.92 14.43 24.88 16.75 36.91 62.9949.37 26.59 17.90 (%) Maximum deformation 7.94 6.71 7.543 9.13 7.5054.23 6.04 3.39 3.83 2.85 level (μm) Restoring speed 1.13 0.921 1.010.788 1.07 0.206 0.223 0.0963 0.193 0.274 (μm/sec) Residual deformation0.523 0.721 0.889 1.668 0.477 1.058 2.256 1.011 0.975 0.429 level (μm)Tan δ (10 Hz) at   25° C. 1.1129 1.0447 1.06457 0.88976 1.0217 0.50520.2631 0.4393 0.413 0.652    0° C. 0.0556 0.0412 0.04374 0.0402 0.03960.0671 0.0847 0.0625 0.0938 0.125 −20° C. 0.0183 0.0113 0.01374 0.012850.0139 0.0235 0.0352 0.0245 0.0275 0.0321 LA (loss area) 31.7 22.7 29.429.5 24.6 27.84 29.02 28.41 26.05 27.74 Storage modulus 4.21E+102.05E+10 4.51E+10 3.26E+10 2.96E+10 2.58E+10 2.52E+10 2.60E+10 2.66E+102.44E+10 (dyne/cm²) (10 Hz: −20° C.) Coefficient of dynamic 0.08 0.140.14 0.13 0.09 0.10 0.09 0.11 0.16 0.11 friction TV setting collapsetest ◯ ◯⁻ ◯⁻ Δ ◯ Δ Δ Δ ◯⁻ ◯⁻ Loading test ◯ ◯ ◯ Δ ◯ X X X Δ Δ (20 g/cm²)Vibration test at   25° C. (10 cycles) ◯ ◯ ◯ ◯ ◯ ◯ ◯ ◯ ◯ ◯    0° C. (5cycles) ◯ ◯ ◯ ◯ ◯ ◯ ◯ ◯ ◯ ◯ −20° C. (3 cycles) Δ Δ X X Δ ◯ ◯ ◯ Δ ◯

TABLE 2 Resin A11 Resin A12 Resin A13 Resin A14 Resin A15 Resin A16Refractive index 1.551 1.548 1.549 1.551 1.551 1.549 (D line)Compression modulus of 535.0 127.40 164.24 200.4 187.86 226.7 elasticity(Mpa) Elastic deformation rate (%) 33.89 60.56 52.244 47.239 46.08 50.52Crosslinking density 1.43E+8  1.47E+8  1.56E+8  1.39E+8  1.67E+8 1.58E+8  (dyne/cm²) (1 Hz: 80° C.) Glass transition temp. (Tp) 27.0 18.021.2 23.7 23.6 26.9 Creep deformation rate (%) 25.44 10.216 13.14615.771 19.932 18.94 Maximum deformation level 3.31 5.69 4.85 5.012 5.4204.467 (μm) Restoring speed (μm/sec) 0.29 1.02 0.94 0.634 0.691 0.579Residual deformation level 0.518 0.245 0.272 0.480 0.501 0.419 (μm) Tanδ (10 Hz) at   25° C. 0.591 0.616 0.616 0.542 0.501 0.487    0° C. 0.1180.172 0.159 0.153 0.156 0.1331 −20° C. 0.0326 0.0393 0.0367 0.041 0.03790.0403 LA (loss area) 27.68 25.97 26.40 26.06 25.13 25.67 Storagemodulus (dyne/cm²) 2.59E+10 2.09E+10 2.32E+10 1.41E+10 9.12E+10 9.76E+10(10 Hz: −20° C.) Coefficient of dynamic friction 0.08 0.10 0.10 0.100.18 0.19 TV setting collapse test ◯⁻ ◯ ◯ ◯ ◯ ◯ Loading test Δ ◯ ◯ ◯ ◯ ◯(20 g/cm²) Vibration test at   25° C. (10 cycles) ◯ ◯ ◯ ◯ ◯ ◯    0° C.(5 cycles) ◯ ◯ ◯ ◯ Δ Δ −20° C. (3 cycles) ◯ ◯ ◯ ◯ X X Resin A17 ResinA18 Resin A19 Resin A20 Resin A21 Resin A22 Refractive index 1.550 1.5511.550 1.520 1.550 1.520 (D line) Compression modulus of 317.62 497.96123.96 212.97 133.2 290.79 elasticity (Mpa) Elastic deformation rate (%)44.957 24.92 54.925 61.004 33.984 61.037 Crosslinking density 2.33E+8 0.859E+8  1.37E+8  2.22E+8  2.02E+7  3.09E+8  (dyne/cm²) (1 Hz: 80° C.)Glass transition temp. (Tp) 26.9 35.0 17.0 5.0 37.5 5.5 Creepdeformation rate (%) 26.742 45.198 15.56 14.71 26.81 15.89 Maximumdeformation level 3.903 4.627 6.159 3.963 10.1 3.20 (μm) Restoring speed(μm/sec) 0.435 0.176 0.904 0.646 1.28 0.523 Residual deformation level0.4978 1.964 0.471 0.278 1.35 0.139 (μm) Tan δ (10 Hz) at   25° C. 0.3720.352 0.538 0.274 0.408 0.243    0° C. 0.119 0.078 0.135 0.273 0.0650.231 −20° C. 0.0344 0.025 0.025 0.155 0.0438 0.1411 LA (loss area)23.01 28.34 25.33 21.96 29.02 20.13 Storage modulus (dyne/cm²) 2.27E+10 2.24E+10 1.37E+10 2.20E+10 1.57E+10 1.73E+10 (10 Hz: −20° C.)Coefficient of dynamic friction 0.15 0.07 0.09 0.09 0.15 0.10 TV settingcollapse test ◯ Δ ◯ ◯ Δ ◯ Loading test ◯ X ◯ ◯ ◯ ◯ (20 g/cm²) Vibrationtest at   25° C. (10 cycles) ◯ ◯ ◯ ◯ ◯ ◯    0° C. (5 cycles) ◯ ◯ ◯ ◯ ◯ ◯−20° C. (3 cycles) ◯ ◯ ◯ ◯ ◯ ◯

TABLE 3 Resin B1 Resin B2 Resin B3 Resin B4 Resin B5 Resin B6 Resin B7Resin B8 Resin B9 Refractive index (D line) 1.552 1.551 1.553 1.5511.549 1.549 1.552 1.551 1.550 Compression modulus 376.6 95.44 188.7323.3 144.0 172.5 411.85 548.75 210.5 of elasticity (Mpa) Elasticdeformation rate 15.47 21.39 21.77 26.05 40.72 34.68 26.895 33.035 23.58(%) Crosslinking density 0.545E+8  0.346E+8  0.33E+8  0.598E+8 0.516E+8  0.592E+8  3.39E+7 9.72E+7  8.18E+7  (dyne/cm²) (1 Hz: 80° C.)Glass transition temp. 29.2 25.6 23.8 23.8 18.9 18.5 40.9 43.4 34.6 (Tp)Creep deformation rate 40.3 32.43 28.54 22.3 10.15 13.27 31.531 37.21658.421 (%) Maximum deformation 8.016 15.72 21.82 5.79 6.73 6.99 6.815.19 9.069 level (μm) Restoring speed 0.256 0.955 1.42 0.411 0.793 0.7010.412 0.220 0.541 (μm/sec) Residual deformation 2.077 1.346 2.204 0.7800.386 0.598 3.452 3.000 1.371 level (μm) Tan δ (10 Hz) at   25° C. 0.630.96 1.144 1.1845 1.2441 1.5321 0.2206 0.2040 0.6331    0° C. 0.06340.043 0.0443 0.0532 0.1415 0.0861 0.089 0.1036 0.1026 −20° C. 0.02420.0195 0.0185 0.0225 0.0348 0.0237 0.0692 0.0792 0.0312 LA (loss area)34.65 37.51 37.94 33.59 33.92 33.04 27.00 28.77 28.71 Storage modulus 2.89E+10  2.87E+10 2.98E+10  2.96E+10  2.60E+10  1.49E+10 8.02E+92.02E+10 3.19E+10 (dyne/cm²) (10 Hz: −20° C.) Coefficient of dynamic0.12 0.12 0.11 0.07 0.11 0.11 0.15 0.14 0.14 friction TV settingcollapse test X X X X X X X X Δ− Loading test X X X X X X X X X (20g/cm²) Vibration test at   25° C. (10 cycles) Δ Δ Δ Δ ◯ ◯ Δ Δ ◯    0° C.(5 cycles) Δ Δ Δ ◯ ◯ Δ ◯ Δ Δ −20° C. (3 cycles) X X X ◯ Δ X ◯ Δ X

TABLE 4 Resin B10 Resin B11 Resin B12 Resin B13 Resin B14 Resin B15Resin B16 Resin B17 Resin B18 Refractive index (D line) 1.551 1.5511.551 1.551 1.551 1.551 1.551 1.551 1.551 Compression modulus 1167.5995.56 1167.5 384.37 221.73 265.3 1160.2 92.4 135.5 of elasticity (Mpa)Elastic deformation rate 11.79 14.78 11.79 14.626 22.45 19.04 22.7928.17 28.02 (%) Crosslinking density 6.71E+7  5.59E+7  4.33E+7  1.23E+7   6E+7 7.87E+7  4.63E+7  2.78E+7  6.57E+7  (dyne/cm²) (1 Hz: 80° C.)Glass transition temp. 38.3 35.5 31.6 34.8 29.4 31.5 34.7 25.3 24.7 (Tp)Creep deformation rate 73.501 51.414 73.501 51.819 30.33 47.15 32.0719.05 19.59 (%) Maximum deformation 10.62 5.51 6.77 8.77 8.27 8.87 2.6411.71 9.12 level (μm) Restoring speed 0.201 0.103 0.203 0.232 0.5060.401 0.102 0.963 0.73 (μm/sec) Residual deformation 6.298 3.08 2.224.27 1.269 1.769 1.203 1.256 1.051 level (μm) Tan δ (10 Hz) at   25° C.0.3649 0.3372 0.4337 0.308 0.7416 0.4503 0.3757 0.9420 1.0456    0° C.0.0386 0.1118 0.0849 0.088 0.071 0.0505 0.074 0.0536 0.0609 −20° C.0.0220 0.1082 0.0673 0.0611 0.0577 0.0214 0.0412 0.0178 0.0228 LA (lossarea) 32.13 36.46 41.51 43.16 33.23 30.02 31.56 35.47 33.10 Storagemodulus 2.76E+10 1.51E+10 1.61E+10 1.62E+10 2.65E+10 3.47E+10 1.64E+102.46E+10 3.60E+10 (dyne/cm²) (10 Hz: −20° C.) Coefficient of dynamic0.13 0.22 0.13 0.14 0.14 0.15 0.12 0.12 0.15 friction TV settingcollapse test X X X X X X X X X Loading test X X X X X X X X X (20g/cm²) Vibration test at   25° C. (10 cycles) Δ X X Δ Δ Δ ◯ Δ ◯    0° C.(5 cycles) Δ X Δ Δ Δ Δ Δ Δ X −20° C. (3 cycles) Δ X Δ Δ Δ X Δ X X

TABLE 5 Resin B19 Resin B20 Resin B21 Resin B22 Resin B23 Resin B24Resin B25 Resin B26 Resin B27 Refractive index (D line) 1.551 1.5511.551 1.551 1.551 1.551 1.551 1.551 1.551 Compression modulus 95.5487.78 121.12 170.68 192.13 254.1 111.46 167.66 132.85 of elasticity(Mpa) Elastic deformation rate 35.34 34.67 25.90 25.07 26.73 22.86 28.1722.50 32.13 (%) Crosslinking density 3.70E+7  3.56E+7  5.98E+7  4.62E+7 2.69E+7  3.51E+7  3.79E+7  6.47E+7  6.77E+7  (dyne/cm²) (1 Hz: 80° C.)Glass transition temp. 24.8 25.5 28.5 25.3 25.2 29.2 26.6 25.9 25.7 (Tp)Creep deformation rate 14.06 17.12 27.40 25.62 20.73 27.80 20.78 29.2918.51 (%) Maximum deformation 6.37 10.35 10.54 8.768 7.647 7.209 10.5879.788 8.444 level (μm) Restoring speed 0.473 1.03 0.733 0.603 0.5950.438 0.789 0.600 0.766 (μm/sec) Residual deformation 1.017 0.759 1.3761.319 0.938 1.225 1.017 1.556 0.822 level (μm) Tan δ (10 Hz) at   25° C.0.8175 0.8491 0.7173 0.7511 0.8156 0.6458 0.984 0.786 0.8511    0° C.0.0958 0.1167 0.1314 0.0932 0.1063 0.049 0.0899 0.085 0.1154 −20° C.0.0268 0.0400 0.1021 0.0309 0.0347 0.0205 0.0277 0.0316 0.0340 LA (lossarea) 31.57 34.00 31.98 33.29 32.54 33.28 33.73 32.26 32.33 Storagemodulus 1.57E+10 3.50E+10 1.88E+10 2.36E+10 1.37E+10 3.38E+10 3.32E+103.89E+10 3.74E+10 (dyne/cm²) (10 Hz: −20° C.) Coefficient of dynamic0.14 0.13 0.20 0.18 0.15 0.14 0.15 0.14 0.14 friction TV settingcollapse test Δ Δ X X X X X X X Loading test X X X X X X X X X (20g/cm²) Vibration test at   25° C. (10 cycles) ◯ ◯ X Δ Δ Δ Δ Δ Δ    0° C.(5 cycles) ◯ Δ X X Δ X X X X −20° C. (3 cycles) ◯ X X X ◯ X X X X

The evaluation and measurement for each item were carried out by thefollowing methods.

Preparation of Samples for Measurement of Dynamic Viscoelasticity

Samples for the measurement of storage modulus, loss tangent, andequilibrium modulus of elasticity as dynamic viscoelasticity wereprepared as follows. A stainless steel plate having a flat surface andcontrolled at 40 to 42° C. was provided as a mold. Each resincomposition regulated to 40 to 42° C. was coated to a thickness of 200μm onto the surface of the mold. Light was applied from a metalhalide-type ultraviolet light lamp (manufactured by Japan StorageBattery Co., Ltd.) to the coating under conditions of integratedquantity of light 2000 mJ/cm² and peak illumination 250 mW/cm² to curethe resin composition. Thereafter, the cured product was separated.Thus, samples for measurement were prepared.

Preparation of Samples for Measurement of Compression Modulus ofElasticity

Samples in a Fresnel lens form for the measurement of compressionmodulus of elasticity were prepared in the same manner as in thepreparation of the samples for the measurement of dynamicviscoelasticity, except that a nickel mold having a surface shape whichis the reverse of the shape of a Fresnel lens was used instead of thestainless steel plate having a flat surface.

Measurement of Dynamic Viscoelasticity

The samples thus obtained were molded into strips having a size of 30mm×3 mm×0.2 mm. 0.0⁵% load strain was applied to the samples with adynamic viscoelasticity measuring device (“RHEOVIBRON,” manufactured byOrientec Co. Ltd.), and the storage modulus and the loss tangent weremeasured. In the measurement, the frequency was 1 to 10 Hz, and thetemperature range was −100 to 100° C. (temperature rise rate 3° C./min).A curve for the dependency of storage modulus upon temperature and acurve for the dependency of loss tangent upon temperature were preparedusing the measured data.

The storage modulus at 25° C. (room temperature), 0° C., and −20° C. wasdetermined from the curve for the dependency of storage modulus upontemperature. Separately, a curve for the dependency of storage modulusupon temperature was prepared in the same manner as described justabove, except that the frequency of force vibration was 1 Hz. Thestorage modulus at 80° C. was determined as an equilibrium modulus ofelasticity from the curve for the dependency of storage modulus upontemperature.

Further, the loss tangent at 25° C. (room temperature), 0° C., and −20°C. was determined from the curve for the dependency of loss tangent upontemperature.

The temperature in a peak position at 1 Hz of the loss tangent (tanδ)was regarded as the glass transition temperature.

Measurement of Coefficient of Dynamic Friction

Samples for the measurement of coefficient of dynamic friction wereprepared in the same manner as in the preparation of the samples for themeasurement of dynamic viscoelasticity, except that the thickness of thecoating was 100 μm and, in the ultraviolet irradiation, the coating wascovered with an acrylic plate. In the measurement, a surface propertymeasuring device (HEIDON TRIBOGEAR TYPE: 14DR, manufactured by ShintoScientific Company Ltd.) was used. A vertical load (a point pressure of100 g) was applied with a ball indenter to the surface of the samples,and the ball indenter was slid on the surface of the sample at a speedof 300 mm/min to measure the coefficient of dynamic friction. Themeasurement was done five times, and the average of the measured valueswas regarded as the coefficient of dynamic friction. The value of themeasurement load divided by the vertical load was regarded as thecoefficient of dynamic friction.

Measurement of Compression Modulus of Elasticity

A universal hardness test using an ultramicrohardness meter (H-100V,manufactured by Fischer, Germany) was applied to calculate thecompression modulus of elasticity. Specifically, the load applied by anindenter was gradually increased to a predetermined value and was thengradually decreased to prepare a curve for the dependency of penetrationdepth upon load, and the results of the measurement were analyzed tocalculate the compression modulus of elasticity. The indenter used was atungsten carbide (WC) ball indenter having a diameter of 0.4 mm.

The curve for the dependency of penetration depth upon load is typicallyas shown in FIG. 2. At the outset, upon a gradual increase in load fromload 0 (point a) to load f, deformation occurs, and the penetrationdepth of the indenter gradually increases. When increasing the load isstopped at a certain load value, penetration caused by plasticdeformation is stopped (point b). Thereafter, the load value is allowedto remain unchanged, during which time the penetration depth continuesto increase due to creep deformation and reaches point c which stops theretention of the load value. Thereafter, as the load is graduallydecreased, the penetration depth decreases toward point d due to elasticdeformation.

In this case, the maximum load value F, which is the load value at pointb in FIG. 2, was set to 20 mN. The reason for this is as follows. In anactual projection screen, the actual measurement of the pressure ofcontact between the Fresnel lens sheet and the lenticular lens sheet isdifficult. However, when the deformation level of the lens constitutingthe screen is about 10 μm on the outer peripheral part of the lens sheetwhich should satisfy a strict requirement, this deformation isacceptable from the viewpoint of lens performance. However, when thecomplexity of the measurement and the dispersion of data due to thedifference in sectional form derived from the shape are taken intoconsideration, the measurement of the deformation around the center (0to 100 mm) which is relatively flat in shape would be preferred. Forthis reason, since the load required for the conventional lens sheet tobe deformed by 10 μm is about 20 mN, 20 mN was used as the maximum loadvalue. The time for creep deformation was arbitrarily brought to 60 sec.

The procedure for determining the curve for the dependency ofpenetration depth upon load is as follows.

-   -   (1) The load value for compression is increased from 0 (zero) to        20 mN in 100 steps every 0.1 sec.    -   (2) The load value increased to 20 mN is maintained for 60 sec        to cause creep deformation.    -   (3) The load value is decreased to 0.4 mN (lowest load in the        tester) in 40 steps every 0.1 sec.    -   (4) The load value 0.4 mN is maintained for 60 sec to recover        the penetration depth.    -   (5) The above steps (1) to (4) are repeated three times.

As shown in FIG. 3, the site on which the ball indenter is allowed toact is preferably around the center part in individual segmented lenssurfaces constituting the Fresnel lens, for example, the center part inparts as indicated by 2c, 2c′, and 2c″. When the spacing betweenadjacent concaves in the lens surface is pitch P, the center part isaround a position corresponding to P/2. Also in the case of other lensshapes, the ball indenter is preferably allowed to act on a positionaround the center of individual lens surfaces constituting the lenses.

The compression modulus of elasticity (E) was determined by thefollowing equation.E=1/(2(hr(2R−hr))^(1/2) ×H×(ΔH/Δf)−(1−n)/e)wherein

-   -   “hr” represents penetration depth at an intersection of a        tangential line with a penetration depth axis (an abscissa) in a        curve, for the dependency of penetration depth upon load, in its        load reduction zone when load f is a maximum value F (unit: mm);    -   “R” represents the radius (2R=0.4 mm) of the ball indenter;    -   “H” represents the maximum value of penetration depth h (unit:        mm);    -   “ΔH/Δf” represents the reciprocal of the slope of a curve, for        the dependency of penetration depth upon load, in its load        reduction zone when load f is a maximum value F;    -   “n” represents the Poisson's ratio of the material (WC) of the        ball indenter (n=0.22); and    -   “e” represents the modulus of elasticity of the material (WC) of        the ball indenter (e=5.3×10⁵ N/mm²).

As described above, increase/decrease of load and the like were repeatedthree times in the order of steps (1), (2), (3), and (4). In this case,for each time of repetition, a curve for the dependency of penetrationdepth upon load was determined, and, based on each of the curves, thecompression modulus of elasticity (E) (unit: Mpa) was determined, andthe average of the values was regarded as the compression modulus ofelasticity.

Maximum Deformation Level and Residual Compression Level

In measuring the compression modulus of elasticity, the deformationlevel at point c shown in FIG. 2 is defined as the maximum deformationlevel.

The deformation level at point e is defined as residual deformationlevel.

Restoring Speed

The restoring speed is defined as follows.V=Δh/Δtwherein Δh represents displacement level at point c in FIG. 2, that is,displacement level 2 sec after the maximum deformation (72 sec after thestart of the test) (μm); and Δt represents restoring time (sec).Creep Deformation Rate

The creep deformation rate (C) was determined by the following equation.C=(h2−h1)·100/h1

-   -   wherein h1 represents penetration depth when the load reaches a        given testing load (20 mN in this case) (point b in FIG. 2)        (unit: mm); and h2 represents penetration depth after a        predetermined period of time (60 sec) has elapsed while holding        the testing load (point c in FIG. 2) (unit: mm).        Elastic Deformation Rate

FIG. 5 is a graph showing a curve for the dependency of penetrationdepth upon load. The elastic deformation rate is the proportion ofelastic deformation energy to total load energy and can be determinedfrom the curve for the dependency of penetration depth upon load shownin FIG. 5. In FIG. 5,

-   -   A: initial state,    -   B: application of maximum load and maximum deformation,    -   B-C: creep deformation level,    -   D: after removal of load (to lowest load),    -   D-E: creep deformation level under lowest load,    -   E-A: residual deformation level, and    -   h_(max)-E: restored deformation level. In this case, the elastic        deformation rate (ηe) can be expressed by        ηe=W _(elastic) /W _(total)        wherein        W _(total) =∫F1(h)dh, and        W _(elastic) =∫F2(h)dh.        Loss Area

In the measurement of dynamic viscoelasticity, the value obtained byintegration in the temperature range of −20 to 50° C. with respect to acurve for the dependency of loss tangent upon temperature at 10 Hz wasregarded as loss area (° C.).

TV Setting Collapse Test

Fresnel lens sheets prepared by molding using the same resincompositions as those used for the measurement of the above compressionmodulus of elasticity (E) and the creep deformation rate (C) were placedso as to face a predetermined lenticular lens sheet, and the four sidesof the assemblies were fixed by a tape, and the fixed assemblies werefitted into wood frames of individual television sizes, followed bymounting on televisions to visually observe and evaluate a white screen.After the elapse of one hr, when collapse of the Fresnel lens sheet wasobserved, the lens sheet was evaluated as “x,” and, when collapse wasnot observed, the lens sheet was evaluated as “∘.” When collapse on aslight level between Δ and ∘ was observed, the lens sheet was evaluatedas “∘⁻.”

Refractive Index

Cured sheets prepared in the same manner as in the samples for dynamicviscoelasticity measurement were provided as samples. Each of thesamples was brought into intimate contact with an Abbe's refractometerin its prism part using 1-bromonaphthalene, and the refractive index wasmeasured with D line (λ=589 nm) at a sample temperature of 25° C. (Forothers, the measurement was done according to JIS K 7105.)

Vibration Test

A Fresnel lens sheet was brought into intimate contact with a lenticularlens sheet so that the lens surface in the Fresnel lens sheet faced thelens surface in the lenticular lens sheet. The four sides of theassembly were fixed by a pressure-sensitive adhesive tape, and the fixedassembly was fitted into a wood frame of TV screen size. This was set ina vibration tester (EDS 252, a vibration tester, manufactured by AkashiCorporation) installed within an environment test chamber kept at aconstant temperature. Random waves having PSD (power spectrum density)waveform shown in FIG. 4 were used for vibration, and a vibration testcorresponding to truck transportation of 5000 km was carried out by 10cycles in the case of a temperature of 25° C., by 5 cycles in the caseof a temperature of 0° C., and by 3 cycles in the case of a temperatureof −20° C. In these cases, 1 cycle was 4320 sec.

The random wave is an indefinite wave having statistic properties whichcan be expressed by PSD function, and, in this vibration test, testconditions are determined using the function as an index. The reason whythe random wave is used is that nonlinear elements of the vibration canbe eliminated, that is, nonlinear elements by mounting of a projectionscreen, a packing form and the like can be eliminated, and the vibrationof the object can be added under given conditions. Further, all thevibrations are different in any point of time base with the test starttime being 0 (zero). Therefore, conditions which are closer tovibrations during actual transportation can be produced.

25° C. (room temperature), 0° C., and −20° C. were used as environmentaltemperatures. After the completion of the test, a screen of which thewhole is white was projected by a projector to inspect the screen foruneven brightness. In this case, when uneven brightness attributable tofriction between lenses was clearly observed, the lens sheet wasevaluated as x; when uneven brightness was observed on a level that isinconspicuous, the lens sheet was evaluated as Δ; and, when unevenbrightness was not observed, the lens sheet was evaluated as ∘.

Loading Test

Fresnel lens sheets prepared by molding using the same resincompositions as those used for the measurement of the above compressionmodulus of elasticity and the creep deformation rate were placed so asto face a predetermined lenticular lens sheet, and the four sides of theassemblies were fixed by a tape, and the fixed assemblies were fittedinto wood frames of individual television sizes, followed by mounting ontelevisions. A pressure of 40 g/cm² was applied to the lenses, and, inthis state, the assemblies were allowed to stand for 10 days at roomtemperature. Thereafter, the load was released. After the release of theload, the white screen of TV was visually inspected and evaluated. Whenthe shape of the lens was restored within 20 min after the release ofthe load and the collapse disappeared, the lens sheet was evaluated as“∘”; when the shape of the lens was restored within 1 to 6 hr after therelease of the load and the collapse disappeared, the lens sheet wasevaluated as “Δ”; and when the collapse disappeared after the elapse of6 hr or longer after the release of the load, or when the shape of thelens was not restored at all even after the elapse of 6 hr or longerafter the release of the load, the lens sheet was evaluated as “x.”

In the above evaluation results, for resin compositions A1 to A18 and B1to B27, a graph in which data on the glass transition temperature (Tg)and the equilibrium modulus of elasticity (CLD) have been plotted isshown in FIG. 6. Further, a graph in which data on the elasticdeformation rate (We) and the compression modulus of elasticity (E) foreach resin composition have been plotted is shown in FIG. 7.

Furthermore, a graph in which data on the compression modulus ofelasticity (E) and the creep deformation rate (C) for each resincomposition have been plotted is shown in FIG. 8.

As is apparent from the evaluation results and each of the graphs, forresins A1 to A5, when the loss tangent (tanδ) at −20° C. is less than0.02 and transportation is made in such a state that optical elementsurfaces are in contact with each other in a low-temperatureenvironment, scratches are likely to occur. (Vibration test)

When resin A2 is compared with resin A3, the storage modulus of resin A2at −20° C. is not more than 2.96×10¹⁰ dyne/cm², whereas the storagemodulus of resin A3 at −20° C. is large and exceeds 2.96×10¹⁰ dyne/cm².Therefore, for resin A3, when transportation is made in such a statethat optical element surfaces are in contact with each other in alow-temperature environment, scratches are likely to occur.

(Vibration Test)

For resin A7, the relationship between the elastic deformation rate (We)and the compression modulus of elasticity (E) is We≦−0.0189E+34.2 anddoes not satisfy the requirement specified in claim 2, and, thus,restorability of the lens from collapse caused by mutual compression ofthe lens surfaces is poor.

Further, for resin A8, the relationship between the compression modulusof elasticity (E) and the creep deformation rate (C) is outside therange specified in claim 6, and, thus, creep properties with respect tocollapse caused by mutual compression of the lens surfaces are so poorthat collapse disadvantageously occurs.

For resins A9, A15, and A16, the coefficient of dynamic friction is notin the range of 0.07 to 0.15 and is above the upper limit of this range,and, thus, scratches are likely to occur during transportation at atemperature around −20° C.

For resins A12, A13, A14, and A17, all the results of evaluation for theTV setting collapse test, the loading test, and the vibration test atvarious temperatures are good.

For resin A18, possibly because the glass transition temperature is theupper limit value 35° C., restorability of the lenses from collapsecaused by mutual compression of the lens surfaces is somewhat poor.

When resins A9, A10, and A11 are compared with each other, it isapparent that, although they have similar material properties (forexample, storage modulus at −20° C., elastic deformation rate, andcompression modulus of elasticity), as the coefficient of dynamicfriction increases, scratches are likely to occur during transportationat a temperature around −20° C.

For resins A11, A18, and B4, although the coefficient of dynamicfriction is in the range of 0.07 to 0.15, the values are close to thelower limit of this range. Therefore, even when the results ofevaluation for the TV setting collapse test and the loading test are notgood, the occurrence of scratches during transportation can beprevented.

For resins B11 and B21, the coefficient of dynamic friction is not lessthan 0.20, and, hence, many scratches are likely to occur duringtransportation in a temperature range of room temperature to lowtemperatures.

For resin B19, according to the evaluation results, the occurrence ofscratches during transportation in a temperature range of roomtemperature to low temperatures can be prevented most effectively.However, good results could not be obtained for the TV setting collapsetest and the loading test.

When resin B23 is compared with resin B25, both the resins have anidentical coefficient of dynamic friction of 0.15. They, however, aregreatly different from each other in occurrence of scratches duringtransportation at a low temperature which is attributable to whether ornot the storage modulus is not more than 2.96×10¹⁰ dyne/cm².Specifically, for resin B23, it is considered that collapse occurs atroom temperature to render the contact area so large that frictionbetween the lenses is likely to occur (i.e., scratches are likely tooccur), while, at a low temperature, the resin is so hard that thecontact area is small and friction between the lenses is less likely tooccur (i.e., scratches are less likely to occur).

FIG. 9 is a graph in which the relationship between the maximumdeformation level and the restoring speed for each resin composition hasbeen plotted based on the evaluation results. FIG. 10 is a graph inwhich the relationship between the residual deformation level and therestoring speed for each resin composition has been plotted.

As shown in FIG. 9, resin compositions A19 to A22 satisfy a relationshiprepresented by formula V≧0.178DM−0.852 wherein V represents restoringspeed, μm/sec, and DM represents maximum deformation level, μm, andprovide good results in the loading test and the vibration test,indicating that collapse of the lens and friction between the lenseshave been reduced.

As is apparent from FIG. 10, resin compositions A19 to A22 satisfy arelationship represented by formula V≧0.858R−0.644 wherein V representsrestoring speed, μm/sec, and R represents residual deformation level,μm, and provide good results in all the loading test and the TV settingcollapse test, and are free from collapse of the lens, have a high levelof lens shape restorability, and a high level of friction resistance.

1. An optical element resin composition for constituting an opticalelement, said resin composition having a glass transition temperature of5 to 36° C. and an equilibrium modulus of elasticity of 0.859×10⁸ to3.06×10⁸ dyne/cm² and satisfying a relationship represented by formulaWe>−0.0189E+34.2 wherein We represents elastic deformation rate in %;and E represents compression modulus of elasticity in Mpa and arelationship represented by formula V≧0.178DM−0.852 wherein V representsrestoration speed in μm/sec; and DM represents maximum deformation levelin μm.
 2. (canceled)
 3. (canceled)
 4. The optical element resincomposition according to any one of claims 1 to 3, wherein therelationship to be satisfied is represented by formula V≧0.112DM−0.236.5. The optical element resin composition according to any one of claims1 to 4, which satisfies a relationship represented by formulaV≧0.858R−0.644 wherein V represents restoration speed in μm/sec; and Rrepresents residual deformation level in μm.
 6. The optical elementresin composition according to any one of claims 1 to 5, which satisfiesa relationship represented by (−0.026E+3)<C<(−0.02E+63) wherein Crepresents creep deformation rate in %; and E represents compressionmodulus of elasticity in Mpa.
 7. The optical element resin compositionaccording to any one of claims 1 to 6, which has a storage modulus ofnot more than 2.96×10¹⁰ dyne/cm² at −20° C. and a loss tangent of notless than 0.02 at −20° C.
 8. The optical element resin compositionaccording to claim 7, wherein the loss area in a temperature range of−20 to 50° C. in a curve for dependency of loss tangent upon temperatureis 20° C. or above.
 9. The optical element resin composition accordingto any one of claims 1 to 8, which has a coefficient of dynamic frictionof 0.07 to 0.15 at room temperature.
 10. (canceled)
 11. (canceled)
 12. AFresnel lens sheet comprising the resin composition according to any oneof claims 1 to 9, said lens sheet having a refractive index of not lessthan 1.52.
 13. A projection screen comprising the optical elementaccording to claim 12 and a lenticular lens.